Substable and pseudo-isotropic processes. Connections with the geometry of subspaces of $L_α$

Misiewicz, Jolanta K.

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Tytuł książki

Substable and pseudo-isotropic processes. Connections with the geometry of subspaces of $L_α$

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Misiewicz Jolanta K.

Seria

Rozprawy Matematyczne tom/nr w serii: 358 wydano: 1996

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CONTENTS
I. Introduction..........................................................................................................5
II. Pseudo-isotropic random vectors........................................................................9
  II.1. Symmetric stable vectors................................................................................9
  II.2. Pseudo-isotropic random vectors..................................................................15
  II.3. Elliptically contoured vectors..........................................................................23
  II.4. α-symmetric random vectors..........................................................................27
  II.5. Substable random vectors.............................................................................32
III. Exchangeability and pseudo-isotropy.................................................................35
  III.1. Pseudo-isotropic exchangeable sequences.................................................35
  III.2. Schoenberg-type theorems..........................................................................40
  III.3. Some generalizations...................................................................................43
IV. Stable and substable stochastic processes.....................................................45
  IV.1. Gaussian processes and Reproducing Kernel Hilbert Spaces....................45
  IV.2. Elliptically contoured processes..................................................................47
  IV.3. Symmetric stable stochastic processes......................................................50
  IV.4. Spectral representation of symmetric stable processes.............................56
  IV.5. Substable and pseudo-isotropic stochastic processes...............................59
  IV.6. $L_α $-dependent stochastic integrals.......................................................62
  IV.7. Random limit theorems...............................................................................63
V. Infinite divisibility of substable stochastic processes..........................................64
  V.1. Infinitely divisible distributions. Lévy measures............................................66
  V.2. Approximative logarithm................................................................................68
  V.3. Infinite divisibility of substable random vectors..............................................73
  V.4. Infinite divisibility of substable processes......................................................77
References...........................................................................................................80
Index......................................................................................................................90

Słowa kluczowe

Tematy

Kategoryzacja MSC:

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Copyright

Seria

Rozprawy Matematyczne tom/nr w serii: 358

Liczba stron

91

Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CCCLVIII

Daty

wydano

1996

otrzymano

1995-03-02

poprawiono

1995-09-18

Twórcy

autor

Misiewicz Jolanta K.

jolanta@graf.im.pwr.wroc.pl

Institute of Mathematics, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

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1991 Mathematics Subject Classification: Primary 46A15, 60B11; Secondary 60G07, 46B20, 60E07, 60K99.

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Substable and pseudo-isotropic processes. Connections with the geometry of subspaces of $L_α$

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